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 Sib. Zh. Ind. Mat., 2012, Volume 15, Number 1, Pages 110–122 (Mi sjim715)

On a precision estimate for a hydrodynamics problem with discontinuous coefficients in the norm of the space $\mathbf L_2(\Omega_h)$

A. V. Rukavishnikov

Khabarovsk Branch, Institute of Applied Mathematics FEB RAS, Khabarovsk, RUSSIA

Abstract: We study the 2-dimensional problem obtained by time-discretizing and linearizing the problem of flow of a 2-phase viscous fluid without mixing in the statement of incompressible Navier–Stokes equations with time-dependent interface. For an approximate solution to this problem we construct a scheme of a nonconformal finite element method. We estimate the rate of convergence of the mesh solution to the exact solution to the problem in the norm of $\mathbf L_2(\Omega_h)$, which agrees with simulations.

Keywords: discontinuous coefficients, domain decomposition, nonconformal finite element method, mortar elements.

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Bibliographic databases:

Document Type: Article
UDC: 519.6
Revised: 04.04.2011

Citation: A. V. Rukavishnikov, “On a precision estimate for a hydrodynamics problem with discontinuous coefficients in the norm of the space $\mathbf L_2(\Omega_h)$”, Sib. Zh. Ind. Mat., 15:1 (2012), 110–122

Citation in format AMSBIB
\Bibitem{Ruk12} \by A.~V.~Rukavishnikov \paper On a~precision estimate for a~hydrodynamics problem with discontinuous coefficients in the norm of the space~$\mathbf L_2(\Omega_h)$ \jour Sib. Zh. Ind. Mat. \yr 2012 \vol 15 \issue 1 \pages 110--122 \mathnet{http://mi.mathnet.ru/sjim715} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3112338}